Dynamic recoil in metamaterials with nonlinear interactions. (May 2022)

• Record Type: Journal Article
• Authors: Liang, Xudong; Crosby, Alfred J.
• Is Part Of: Journal of the mechanics and physics of solids. Volume 162(2022)
• Publication Date: 2022-05
• Subjects: Metamaterials -- Solitary waves -- Nonlinear waves -- Recoil -- Sonic vacuum; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.104834
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: Biological systems can generate motions with high acceleration and velocity via dynamic recoil. Traditionally, recoil dynamics in unstructured linear elastic systems are based on inertial and elastic properties, with the recoil velocity determined by the materials' speed of sound and the strain at recoil. Metamaterials with designed elastic structures and nonlinear interactions (e.g., magnetic interactions) have recently demonstrated the capability to control impulsive motions and manage high-rate energy transfer events. However, a predictive model for understanding the kinematics and recoil dynamics has not been developed. Here, we study the dynamic recoil that couples with a general nonlinear power-law interaction within a metamaterial framework. Starting with a 1D discrete model, we demonstrate how the nonlinear force interactions and the elastic structures in metamaterials control the dynamic performance. Under a weakly nonlinear condition, the governing equation of the dynamic recoil is described by the KdV (Korteweg-de Vries) equation and under the condition of strong nonlinearity by a more general strongly nonlinear wave equation. Our model predicts a "sonic vacuum" response in the recoiling metamaterials, where a near-zero speed of sound is induced by strongly nonlinear interactions and zero initial prestress. We propose a sequential wave motion during the dynamic recoil, where a linear wave propagates at a large stretch and switches to a nonlinear one below a critical stretch. We further discover that the nonlinear wave speed has a non-monotonic dependence upon the strength of the power-law interaction. We find good agreements in the recoil velocity by comparing our analytical model to experiments of the recoiling metamaterials with magnetic interactions. Our work demonstrates how power-law interactions within metamaterials can program dynamic recoil dynamics, setting the stage for new materials designs for energy management and conversion in high-rate applications.